It is the season for columns pleading for the appearance of Leo McGarry in Downing Street. McGarry, played by the late John Spencer, was the hugely effective and ever courteous White House chief of staff in the fictional West Wing.

A series of mishaps in Downing Street has prompted the latest round of columns calling for David Cameron to get a grip over his operation.

Martin Ivens in yesterday's Sunday Times ran the latest in his regular series of 'Dave needs a proper chief of staff' columns. And over at the Telegraph today James Kirkup suggests that Cameron is a little too laid back and should get a grip.

All the columns have rightly identified a clear problem in No 10. Contentious policies, which should have been stress-tested, appear from a clear blue sky and shake Downing Street.

The two obvious examples are the proposals to sell the forests and Andrew Lansley's plans to hand 80% of the NHS's £100bn budget to GP commissioning consortia. It is clear what caused the problems in both these cases:

• Forests. Caroline Spelman, the environment secretary, is so insecure about her position in the cabinet that she offered up vast areas of her budget for cuts to win a place on the "star chamber" ahead of the autumn spending round.

• Health. Cameron is so determined to avoid micro-managing departments in the style of Tony Blair that he left the formulation of the most significant shake up in the NHS in decades to Lansley. The prime minister took fright at the scale of the reforms in the autumn and despatched his policy guru Oliver Letwin to look over Lansley's shoulder. Downing Street is now apparently reassured.

The problems over forests and health are likely to be resolved by a change in the policy unit at No 10. Patrick Wintour and I reported in December that Cameron is to reorganise the Downing Street policy unit along similar lines to Blair's operation to ensure that individual policy experts monitor particular departments.

But there is a deeper problem. The supposedly slick Cameron operation has not grasped the significance of strategy and the importance of strategic communications. This explains why people are not doing the jobs which their job descriptions suggest they should be doing.

This confusion is embodied in Steve Hilton who is officially the Downing Street director of strategy. That is not what Hilton does. Hilton is in reality the director of blue skies thinking.

It is wrong to suggest that Hilton, who walks round Downing Street in his cycling shorts even in winter, is a wacky tree-hugger divorced from reality. He is a wordsmith who can transform policy documents in some of the more dreary areas of government. But Hilton is more of a dreamer whose great idea, the Big Society, can politely be described as a work in progress.

Downing Street does technically have a Leo McGarry figure. Ed Llewellyn, a much loved and much admired member of the Cameron inner circle for years, is the chief of staff who commands widespread respect in Whitehall But his greatest strength is as Cameron's chief foreign policy adviser. Llewellyn deserves credit for the transformation in relations between Cameron and leaders across the EU since the election.

A chief of staff and a director of strategy should ideally work closely with a communications director as they shape a strategy for the government. Put simply, these three figures should decide where the government wants to be in one, two, three five or six years time and work out to get there.

That hasn't happened because Hilton and Llewellyn don't really occupy those roles. There has been an added complication. Hilton was barely on speaking terms with Andy Coulson, the No 10 director of communications until last week.

Two reasons explained the Coulson-Hilton tensions. First, the former tabloid editor was deliberately chosen by Cameron as a counterweight to Hilton. Second, Coulson was not a great long term, strategic thinker.

Coulson's handpicked successor, the former BBC News at Ten editor Craig Oliver, will no doubt run a highly professional operation in No 10, as his predecessor did. But his challenge will be to show that someone who has barely shown any interest in politics can help craft a strategy and a message that will show to the British electorate in 2015 that the Tories have a vision for the future. This is the job Alastair Campbell did highly effectively for Labour until he lost his judgment in the run up to the Iraq war.

Watching this process with care will be the key figure who is in reality the Downing Street chief of staff and director of strategy – George Osborne. Cameron relies on Osborne in the way that no prime minister has relied on a fellow cabinet minister since Margaret Thatcher had her Willie (Whitelaw) in the 1980s.

Osborne has a day job as chancellor which means that he cannot focus on his evening jobs as director of strategy and chief of staff. But he is only too happy to fill the void because it entrenches his position.

So back to those Leo McGarry columns. The most significant column did not actually call for a chief of staff. It instead called for a chief idea.

Daniel Finkelstein wrote in his weekly Times column on 26 January that the government's central strategy – to stabilise the public finances by eliminating the structural deficit by the end of this parliament – is not enough to win the election. Finkelstein said the government needs to work hard on hammering out a strategy and a vision for what it will do after the train, the Good Great Britain, arrives at its destination of stabilised public finances.

Finkelstein is close to Osborne from their days working for William Hague. He is the perfect candidate to fill the gaps in Downing Street. But he would be a great loss to journalism.